Inference within Knowledge

Abstract

This paper applies the the technique of Game Logic GL! , which has recently been formulated by Kaneko and Nagashima, to Mccarthy's Three Wise Men Puzzle. The analysis makes it clear what one really knows when he or she knows it impossible to know something as well as how one can enrich his or her knowledge by knowing that someone else knows it impossible to know something. The point is that human being is capable of jumping out from the logical system within which he or she makes inferences; this may well have significant implications for the analysis of human behaviour. 1 Introduction There have been interests in formal treatment of games which involve the notion of knowledge. A first comprehensive treatment of logical systems with knowledge operator is seen in [?]. Another epochmaking achievement is seen in [?] and [?], in which the authors formulate the notion of common knowledge as an infinite conjunction of all possible states of knowledge of finite number of players, an..